U-HNSW: An Efficient Graph-based Solution to ANNS Under Universal Lp Metrics
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911654329974784 |
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| author | Wang, Huayi Meng, Jingfan Xu, Jun |
| author_facet | Wang, Huayi Meng, Jingfan Xu, Jun |
| contents | Approximate nearest neighbor search under universal L_p metrics (ANNS-U-L_p) is an important and challenging research problem, as it requires answering queries under all possible p (0<p <= 2) values simultaneously without building an index for each possible p value. The state-of-the-art solution, called MLSH, is a Locality-Sensitive Hashing (LSH)-based ANNS method with barely acceptable query performance. In contrast, graph-based ANNS methods, which offer significantly improved query efficiency on the ANNS-L_p problem (with a fixed p-value), cannot be naively extended to the ANNS-U-$L_p$ problem. In this paper, we propose U-HNSW, the first graph-based method for ANNS-U-L_p. Our scheme uses HNSW graph indexes built on two base metrics ($L_1$ and $L_2$) to generate promising nearest neighbors candidates, and then verifies these candidates with an early-termination strategy that substantially reduces the number of expensive L_p distance computations. Experimental results show that U-HNSW not only achieves up to 2670 times shorter query times than the original MLSH implementation running on a RAM disk (up to 15 times shorter than the idealized MLSH), but also outperforms the original HNSW on the ANNS-L_p problem (with a fixed p-value), except for a few special p values. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_02030 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | U-HNSW: An Efficient Graph-based Solution to ANNS Under Universal Lp Metrics Wang, Huayi Meng, Jingfan Xu, Jun Databases Data Structures and Algorithms Approximate nearest neighbor search under universal L_p metrics (ANNS-U-L_p) is an important and challenging research problem, as it requires answering queries under all possible p (0<p <= 2) values simultaneously without building an index for each possible p value. The state-of-the-art solution, called MLSH, is a Locality-Sensitive Hashing (LSH)-based ANNS method with barely acceptable query performance. In contrast, graph-based ANNS methods, which offer significantly improved query efficiency on the ANNS-L_p problem (with a fixed p-value), cannot be naively extended to the ANNS-U-$L_p$ problem. In this paper, we propose U-HNSW, the first graph-based method for ANNS-U-L_p. Our scheme uses HNSW graph indexes built on two base metrics ($L_1$ and $L_2$) to generate promising nearest neighbors candidates, and then verifies these candidates with an early-termination strategy that substantially reduces the number of expensive L_p distance computations. Experimental results show that U-HNSW not only achieves up to 2670 times shorter query times than the original MLSH implementation running on a RAM disk (up to 15 times shorter than the idealized MLSH), but also outperforms the original HNSW on the ANNS-L_p problem (with a fixed p-value), except for a few special p values. |
| title | U-HNSW: An Efficient Graph-based Solution to ANNS Under Universal Lp Metrics |
| topic | Databases Data Structures and Algorithms |
| url | https://arxiv.org/abs/2605.02030 |